Adaptive filter

ABSTRACT

An adaptive filter includes: a filter configured to perform a filtering process for an input signal with a filter coefficient set therein, and output the processed input signal as an output signal; a calculating unit configured to calculate a value indicative of an error between an amplitude of the output signal and a reference amplitude; an output unit configured to output a first constant as a parameter when the amplitude of the output signal is greater than the predetermined amplitude, the parameter used when updating the filter coefficient, and output a second constant as the parameter when the amplitude of the output signal is smaller than the predetermined amplitude; and an updating unit configured to update the filter coefficient with an update amount corresponding to the parameter and the value indicative of the error, such that the error is reduced.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to Japanese PatentApplication No. 2011-146302, filed Jun. 30, 2011, of which full contentsare incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an adaptive filter.

2. Description of the Related Art

In an adaptive filter, a step size parameter μ having a great value maybe used to reduce a convergence time period for a filter coefficient toconverge to a proper value. However, when the step size parameter μ isunnecessarily increased in value, the filter coefficient may notconsequently converge and may significantly deviate from its optimalvalue. Thus, the value of the step size parameter μ is determinedconsidering the balance between whether the filter coefficient convergesin value and the convergence time period (see, e.g., Japanese Laid-OpenPatent Publication No. 2002-261528).

For example, an adaptive filter configured to operate based on a CMA(Constant Modulus Algorithm) has a filter coefficient whose updateamount varies with not only the step size parameter μ but also theamplitude of an output signal outputted from the adaptive filter. Theamplitude of the output signal outputted from the adaptive filter varieswith the amplitude of an input signal inputted to the adaptive filter.Therefore, when the amplitude of the input signal inputted to theadaptive filter significantly fluctuates, it is difficult to properlycontrol the update amount of the filter coefficient.

SUMMARY OF THE INVENTION

An adaptive filter according to an aspect of the present invention,includes: a filter configured to perform a filtering process for aninput signal with a filter coefficient set therein, and output theprocessed input signal as an output signal; a calculating unitconfigured to calculate a value indicative of an error between anamplitude of the output signal and a reference amplitude; an output unitconfigured to output a first constant as a parameter when the amplitudeof the output signal is greater than the predetermined amplitude, theparameter used when updating the filter coefficient, and output a secondconstant as the parameter when the amplitude of the output signal issmaller than the predetermined amplitude; and an updating unitconfigured to update the filter coefficient with an update amountcorresponding to the parameter and the value indicative of the error,such that the error is reduced.

Other features of the present invention will become apparent fromdescriptions of this specification and of the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

For more thorough understanding of the present invention and advantagesthereof, the following description should be read in conjunction withthe accompanying drawings, in which:

FIG. 1 is a diagram illustrating a configuration of an adaptive filter10 according to a first embodiment of the present invention;

FIG. 2 is a diagram illustrating a configuration of an FIR filter 20;

FIG. 3 is a diagram illustrating a configuration of a variable outputunit 23;

FIG. 4 is a diagram for explaining updating of a filter coefficient W(n)when “μ1” is greater than “μ2”;

FIG. 5 is a diagram for explaining updating of the filter coefficientW(n) when “μ1” is greater than “μ2”;

FIG. 6 is a diagram illustrating a configuration of an FM radio receiver100 using an adaptive filter 10 as an equalizer;

FIG. 7 is a diagram for explaining an operation of an adaptive filter 10(equalizer) when multipath occurs;

FIG. 8 is a diagram illustrating a configuration of an adaptive filter15 according to a second embodiment of the present invention; and

FIG. 9 is a diagram for explaining an operation of an adaptive filter 15(equalizer) when multipath occurs.

DETAILED DESCRIPTION OF THE INVENTION

At least the following details will become apparent from descriptions ofthis specification and of the accompanying drawings.

Adaptive Filter 10 First Embodiment

FIG. 1 is a diagram illustrating a configuration of an adaptive filter10 according to a first embodiment of the present invention. Theadaptive filter 10 operates based on the CMA, and updates a filtercoefficient thereof such that the magnitude of the amplitude of anoutput signal y(n) becomes equal to the target magnitude of a referenceamplitude “A”. The adaptive filter 10 is realized by a DSP (DigitalSignal Processor), for example, and includes an FIR (Finite ImpulseResponse) filter 20, a level detecting unit 21, an error calculatingunit 22, a variable output unit 23, and a coefficient updating unit 24.

As depicted in FIG. 2, the FIR filter 20 is a filter configured toexecute a convolution on an input signal x(n) and a filter coefficientW(n) (W=[w1, w2, . . . , wk]^(T)), and includes delay devices D1 to Dk,multipliers M1 to Mk, and an adder 30.

The delay device D1 outputs a signal x(n−1) obtained by delaying theinput signal x(n) by one sampling time period. The multiplier M1multiplies the signal x(n−1) by a filter coefficient w1, and outputs aresultant signal. The delay devices D2 to Dk are similar to the delaydevice D1. The multipliers M2 to Mk are similar to the multiplier M1.

The adder 30 adds up signals outputted from the multipliers M1 to Mk andoutputs a resultant signal as the output signal y(n). Therefore, theoutput signal y(n) is expressed by Equation (1) as follows.

$\begin{matrix}{{y(n)} = {\sum\limits_{m = 1}^{k}{w_{m} \times {x\left( {n - m} \right)}}}} & (1)\end{matrix}$

The level detecting unit 21 calculates a value indicative of themagnitude of the amplitude of the output signal y(n) (for example,|y(n)|).

The error calculating unit 22 (calculating unit) calculates a valueindicative of an error between the amplitude of the output signal y(n)and the reference amplitude “A”, as an evaluation function E(n).Specifically, the error calculating unit 22 calculates the evaluationfunction E(n) based on Equation (2).

E(n)=(|y(n)|^(p) −A ^(p))^(q)  (2)

In an embodiment of the present invention, it is assumed that each of“p” and “q” in Equation (2) is “two”.

The variable output unit 23 (output unit) outputs a step size parameterμ(n) that corresponds to the amplitude of the output signal y(n).

The coefficient updating unit 24 (updating unit) updates the filtercoefficient W(n) based on the evaluation function E(n) and the step sizeparameter μ(n). Specifically, the coefficient updating unit 24 updatesthe filter coefficient W(n) based on an algorithm of a steepest-descentmethod, for example, such that the value of the evaluation function E(n)becomes the smallest. On this occasion, the coefficient updating unit 24calculates the filter coefficient W(n) based on Equation (3), forexample.

$\begin{matrix}{{W\left( {n + 1} \right)} = {{W(n)} - {{\mu (n)}\begin{bmatrix}\frac{\partial{E(n)}}{{\partial w}\; 1} \\\vdots \\\frac{\partial{E(n)}}{\partial{wk}}\end{bmatrix}}}} & (3)\end{matrix}$

Here, when substituting Equation (2) where p=2 and q=2 into Equation(3), Equation (4) is obtained.

W(n+1)=W(n)−4μx(n)y*(n)(|y(n)|² −A ²)  (4)

In Equation (4), y*(n) is a complex conjugate number of y(n). As isclear from Equation (4), the update amount (W(n+1)−W(n)) of the filtercoefficient W(n) increases as the step size parameter μ(n) increases. Assuch, the relationship of Equation (1) is established between the outputsignal y(n) and the input signal x(n). Therefore, even if the value ofthe step size parameter μ(n) is constant, for example, when theamplitude of the input signal x(n) increases and a value (|y(n)|²−A²)indicative of the error increases, the update amount of the filtercoefficient also increases.

==Details of Variable Output Unit 23==

The details of the variable output unit 23 will be described withreference to FIG. 3. The variable output unit 23 includes a detectingunit 40, a timer 41, storing units 42 and 43, and a selecting unit 44.The timer 41, the storing units 42 and 43, and the selecting unit 44 areequivalent to a parameter output unit.

The detecting unit 40 detects whether the amplitude of the output signaly(n) is greater than the predetermined amplitude B (>the referenceamplitude A) based on the value |y(n)|² indicative of the magnitude ofthe amplitude of the output signal y(n).

The timer 41 determines whether the predetermined time period TA haselapsed from the time when the detecting unit 40 detects that theamplitude of the output signal y(n), which was greater than thepredetermined amplitude B, decreases and becomes smaller than thepredetermined amplitude B. The timer 41 includes a counting unit 50 anda determining unit 51.

The counting unit 50 updates (for example, decrements) a set count valueCNT every sampling time period. The counting unit 50 includes a countvalue storing unit 60, a selecting unit 61, an updating unit 62, anadder 63, and a delay device 64.

The count value storing unit 60 has the predetermined count value C1stored therein. The selecting unit 61 selects the count value C1 storedin the count value storing unit 60 and outputs the count value C1 to theadder 63 when it is detected that the amplitude of the output signaly(n) is greater than the predetermined amplitude B. The selecting unit61 outputs the count value CNT stored in the delay device 64 to theadder 63 when it is detected that the amplitude of the output signaly(n) is smaller than the predetermined amplitude B.

The updating unit 62 and the adder 63, every sampling time period,subtract (decrement) “one” from the count value outputted from theselecting unit 61, and store the resultant count value in the delaydevice 64.

Therefore, the counting unit 50 is set at a count value C1-1 (firstpredetermined value) as the count value CNT every time it is detectedthat the amplitude of the output signal y(n) is greater than thepredetermined amplitude B.

The determining unit 51 determines whether the count value CNT isdecremented from the count value C1-1 and reaches the predeterminedcount value C2 (second predetermined value). It is assumed that the timeperiod until the time when the count value CNT to reach the count valueC2 by being decremented from the count value C1-1 by one every decrementis the predetermined time period TA.

The storing units 42 and 43 have step size parameters μ1 and μ2 storedtherein, respectively. The relationship between the values of the stepsize parameters μ1 (first constant) and μ2 (second constant) will bedescribed later.

The selecting unit 44 selects and outputs the step size parameter μ1when the count value CNT is smaller than the count value C1 that isgreater than the count value C2, that is, during a time period from thetime when the amplitude of the output signal y(n) decreases and becomessmaller than the predetermined amplitude B to the time when thepredetermined time period TA has elapsed therefrom. The selecting unit44 selects and outputs the step size parameter μ2 when the count valueCNT is equal to or smaller than the count value C2, that is, forexample, when the predetermined time period TA has elapsed from when theamplitude of the output signal y(n) becomes smaller than thepredetermined amplitude B. In an embodiment of the present invention, itis assumed that the initial value of the count value CNT is the countvalue C2. Therefore, when the adaptive filter 10 is started, the stepsize parameter μ2 is selected and outputted.

==Updating of Filter Factor W(n) (When μ1<μ2)==

An update amount of the filter coefficient W(n) will be described forthe case where the amplitude of the input signal X(n) increases on thecondition that the value of the step size parameter μ2 usually used isgreat to some extent and is greater than the step size parameter μ1.

Here, a description will be made using the evaluation function E(n)where p=1 and q=2 for convenience sake. The evaluation function E(n)where p=1 and q=2 is a quadratic function of the filter coefficientW(n), as is clear from the relationship of Equations (1) and (2).Therefore, the relationship between the evaluation function E(n) and thefilter coefficient W(n) is expressed as a downwardly convex quadriccurve as depicted in FIG. 4, for example. Furthermore, in FIG. 4, theorigin point is set at a point at which the evaluation function E(n) isthe minimum (optimum point) for convenience sake.

For example, when the current filter coefficient W(n) is a coefficientdetermined at “A point”, that is, when “A point” is present in thepositive region, the slope of the evaluation function E(n) at “A point”is positive as is clear from Equation (3). Therefore, the update amountof the filter coefficient W(n) is a negative value and the filtercoefficient W(n) is updated toward the optimum point (origin point).

Here, in the case where the filter coefficient W(n) is the coefficientdetermined at “A point”, when the amplitude of the input signal x(n)becomes greater than the predetermined amplitude B, the value indicativeof the error (|y(n)|−A) in Equation (4) also increases as describedabove. In this case, when μ2 (>μ1) having a great value continues to betentatively used as the step size parameter μ(n), the update amountincreases and the filter coefficient W(n+1) may move from “A point” to“B point”, for example, passing the origin point. That is, the filtercoefficient W(n) becomes difficult to converge.

However, in this case, when the amplitude of the input signal x(n)becomes greater than the predetermined amplitude B, μ1 having a smallvalue is used as the step parameter μ(n). Therefore, in this case, it issuppressed that the update amount unnecessarily increases. Therefore, asdepicted in FIG. 4, the filter coefficient W(n+1) moves from “A point”to “C point”, for example, which enables the filter coefficient W(n+1)to approach the origin point that is the optimum point in a more stablemanner.

==Updating of Filter Factor W(n) (When μ1>μ2)==

An update amount of the filter coefficient W(n) will be described forthe case where the amplitude of the input signal X(n) increases on thecondition that the value of the step size parameter μ2 usually used issmall to some extent and is smaller than the step size parameter μ1.

Here, in the case where the filter coefficient W(n) is a coefficientthat is determined at “X point” of FIG. 5, when the amplitude of theinput signal x(n) becomes greater than the predetermined amplitude B,the value (|y(n)|−A) indicative of the error also increases as describesabove. When μ2 (<μ1) having a small value continues to be tentativelyused as the step parameter μ(n), the update amount remains small.Therefore, the filter coefficient W(n+1) may only move from “X point” to“Y point” that is close to “X point”, for example. That is, theconvergence time period of the filter coefficient W(n) may become verylong.

However, in this case, μ1 having a great value is used as the stepparameter μ(n) when the amplitude of the input signal x(n) becomesgreater than the predetermined amplitude B. Therefore, in this case, theupdate amount can be increased. As depicted in FIG. 5, the filtercoefficient W(n+1) moves from “X point” to “Z point”, for example, whichenables the filter coefficient W(n+1) to approach the origin point thatis the optimum point in a quicker manner.

It should be noted that the description has been made using theevaluation function E(n) where p=1 and q=2 for convenience sake in theabove, but the same applies to the case where p=2 and q=2.

<<<Application of Adaptive Filter 10>>>

FIG. 6 is a diagram illustrating the configuration of an FM radioreceiver 100 applied with the adaptive filter 10 of FIG. 1 as anequalizer.

The FM radio receiver 100 includes the adaptive filter 10, a tuner 110,an AD converter 111, an IF filter 112, and an FM demodulator 113.

The tuner 110 produces an IF (InteLmediate Frequency) signal at anintermediate frequency from a broadcast signal received through anantenna.

The AD converter (ADC: Analog Digital Converter) 111 digitizes the IFsignal. The IF filter 112 selects and outputs a signal (channel) in adesired frequency band from the signal outputted from the AD converter111.

The adaptive filter 10 equalizes the signal outputted from the IF filter112 (hereinafter, referred to as “input signal X(n)”) and outputs theequalized signal. Specifically, the adaptive filter 10 updates thefilter coefficient W(n) such that the amplitude of the output signaly(n) becomes constant. The FM demodulator 113 demodulates the outputsignal y(n) and reproduces the demodulated signal using a speaker.

==Operation of Adaptive Filter 10 When Multipath Occurs==

A description will be given of an operation of the adaptive filter 10when multipath occurs during a time period from a time t0 to around atime t4, for example, (a time period between the times t4 and t5, forexample) with reference to FIG. 7. In FIG. 7, the axis of ordinaterepresents a value |y(n)| indicative of the magnitude of the amplitudeof the output signal y(n) and the axis of abscissas represents the time.In this case, it is assumed that the value of the step size parameter μ1is smaller than the value of the step size parameter μ2.

For example, when the multipath occurs at the time t0, the amplitude ofthe IF signal fluctuates which should be originally constant. Therefore,the amplitudes of the input signal X(n) and the output signal y(n) alsofluctuate associated with the fluctuation of the amplitude of the IFsignal.

When the amplitude of the output signal y(n) becomes greater than thepredetermined amplitude B at a time t1, the step size parameter μ1 (<μ2)is outputted. Therefore, variation of the update amount of the filtercoefficient W(n) is suppressed even when the amplitude of the inputsignal X(n) increases.

The amplitude of the output signal y(n) becomes smaller than thepredetermined amplitude B at a time t2. However, at a time t3 at thetime when the predetermined time period TA does not elapse from the timet2, the amplitude of the output signal y(n) again becomes greater thanthe predetermined amplitude B. Therefore, the step size parameter μ1having the small value continues being outputted.

Thereafter, the influence of the multipath becomes weak.

The amplitude of the output signal y(n) becomes smaller than thepredetermined amplitude B at a time t4. At a time t5 after thepredetermined time period TA has elapsed from the time t4, the step sizeparameter μ2 having the great value is outputted. As a result, theadaptive filter 10 is able to update the filter coefficient W(n) in astable manner even during the occurrence of the multipath. The influenceof the multipath is suppressed since the adaptive filter 10 updates thefilter coefficient W(n) such that the amplitude of the output signaly(n) becomes constant.

Adaptive Filter 15 Second Embodiment

FIG. 8 is a diagram illustrating the configuration of an adaptive filter15 according to a second embodiment of the present invention. Comparingthe adaptive filter 15 with the adaptive filter 10 of FIG. 1, theconfigurations thereof are similar except for a variable output unit 25.

The variable output unit 25 (output unit) outputs a value indicative ofan error based on the value of the evaluation function E(n) and the stepsize parameter μ(n) that corresponds to the amplitude of the outputsignal y(n). The variable output unit 25 uses a detecting unit 80 inplace of the detecting unit 40 of the variable output unit 23 asdepicted in FIG. 3, for example. Comparing the variable output unit 25with the variable output unit 23, the configurations thereof are similarexcept for the detecting unit 80 denoted by a bracketed referencenumeral in FIG. 3.

The detecting unit 80 determines whether the value of the evaluationfunction E(n) is greater than the predetermined value C when theamplitude of the output signal y(n) reaches the predetermined amplitudeB.

The configuration of the variable output unit 25 except for thedetecting unit 80 is similar to that of the variable output unit 23, andtherefore the selecting unit 44 selects and outputs the step sizeparameter μ1 from the time when the amplitude of the output signal y(n)becomes smaller than the predetermined amplitude B to the time when thepredetermined time period TA has elapsed. The selecting unit 44 selectsand outputs the step size parameter μ2 when the predetermined timeperiod has elapsed after the amplitude of the output signal y(n) becomessmaller than the predetermined amplitude B, for example.

==Operation of Adaptive Filter 15==

FIG. 9 is a diagram for explaining an operation of the adaptive filter15 executed when the adaptive filter 15 is used as an equalizer in theFM radio receiver 100. In this case, it is assumed that multipath occursduring a time period from a time t10 to around a time t12, for example(a time period between times t12 and t13 for example). In FIG. 9, theaxis of ordinate represents the value of the evaluation function E(n)(the value indicative of the error) and the axis of abscissas representsthe time. In this case, it is assumed that the value of the step sizeparameter μ1 is smaller than the value of the step size parameter μ2usually used.

For example, when the multipath occurs at the time t10, the amplitude ofthe input signal X(n) significantly fluctuates. When the value of theevaluation function E(n) becomes greater than the predetermined value Cat a time t11, the step size parameter μ1 (<μ2) is outputted. Therefore,variation of the update amount of the filter coefficient W(n) issuppressed even when the amplitude of the input signal X(n) increases.

During a time period from the time t11 to the time t12, although thevalue of the evaluation function E(n) fluctuates, the predetermined timeperiod TA does not elapse from the time when the value of the evaluationfunction E(n) has become smaller than the predetermined value C.Therefore, during this time period, the step size parameter μ1 havingthe small value continues being outputted. Then, for example, theinfluence of the multipath becomes weak, and at a time t13 when thepredetermined time period TA has elapsed from the time t12 at which thevalue of the evaluation function E(n) has become smaller than thepredetermined value C, the step size parameter μ2 having the great valueis outputted.

As a result, the adaptive filter 15 is able to update the filtercoefficient W(n) in a stable manner even during the occurrence of themultipath. The influence of the multipath is suppressed since the filtercoefficient W(n) is updated such that the amplitude of the output signaly(n) becomes constant.

The adaptive filters 10 and 15 according to embodiments of the presentinvention have been described. The adaptive filter 10 outputs the stepsize parameter μ2 when the amplitude of the input signal X(n) is smalland that of the output signal y(n) is also small, and outputs the stepsize parameter μ1 when the amplitude of the input signal X(n) increasesand that of the output signal y(n) also increases. Therefore, theadaptive filter 10 is able to properly control the update amount of thefilter coefficient W(n) even when the amplitude of the input signalsignificantly fluctuates.

For example, the filter coefficient W(n) is able to converge in a stablemanner by reducing the value of the step size parameter μ1 at a valuesmaller than the value of the step size parameter μ2.

When the step size parameter μ2 is outputted immediately after theamplitude of the output signal y(n) decreases and becomes smaller thanthe predetermined amplitude B, in the case where the amplitude of theoutput signal y(n) significantly fluctuates in a short time period, theupdate amount of the filter coefficient W(n) may become unstable and maynot converge. In embodiments of the present invention, the step sizeparameter μ2 is outputted after the predetermined time period TA haselapsed from the time when the amplitude of the output signal y(n) hasbecome smaller than the predetermined amplitude B. Therefore, forexample, even when the amplitude of the output signal y(n) significantlyfluctuates in a short time period due to the influence of the multipath,etc., the filter coefficient W(n) can be updated in a stable manner.

Further, since the predetermined time period TA is determined based onthe count values C1 and C2, the predetermined time period TA can beeasily varied.

The adaptive filter 15 varies the value of the step size parameter μ(n)based on the value of the evaluation function E(n) indicative of theerror. Even in this case, the update amount of the filter coefficientW(n) can be properly controlled.

In embodiments of the present invention, the steepest-descent method isused as the algorithm to update the filter coefficient W(n). However,another algorithm may be used such as Marquardt Method (non-linear leastsquare algorithm).

Although it is assumed that “p” and “q” is set at two in the evaluationfunction E(n), other values (for example, p=2 and q=1) may be used.

The above embodiments of the present invention are simply forfacilitating the understanding of the present invention and are not inany way to be construed as limiting the present invention. The presentinvention may variously be changed or altered without departing from itsspirit and encompass equivalents thereof.

1. An adaptive filter comprising: a filter configured to perform afiltering process for an input signal with a filter coefficient settherein, and output the processed input signal as an output signal; acalculating unit configured to calculate a value indicative of an errorbetween an amplitude of the output signal and a reference amplitude; anoutput unit configured to output a first constant as a parameter whenthe amplitude of the output signal is greater than the predeterminedamplitude, the parameter used when updating the filter coefficient, andoutput a second constant as the parameter when the amplitude of theoutput signal is smaller than the predetermined amplitude; and anupdating unit configured to update the filter coefficient with an updateamount corresponding to the parameter and the value indicative of theerror, such that the error is reduced.
 2. The adaptive filter of claim1, wherein the first constant is smaller in value than the secondconstant.
 3. The adaptive filter of claim 2, wherein the output unitincludes: a detecting unit configured to detect whether the amplitude ofthe output signal is greater than the predetermined amplitude or not;and a parameter output unit configured to, based on a detection resultof the detecting unit, output the first constant as the parameter from atime when the amplitude of the output signal has become smaller than thepredetermined amplitude until a time when the predetermined time periodhas elapsed, and output the second constant as the parameter when thepredetermined time period has elapsed from the time when the amplitudeof the output signal has become smaller than the predeterminedamplitude.
 4. The adaptive filter of claim 3, wherein the parameteroutput unit includes: a storing unit configured to store the first andthe second constants; a counting unit configured to update a count valueat predetermined time intervals, the counting unit having a firstpredetermined value set therein as the count value every time thedetecting unit outputs a detection result indicating that the amplitudeof the output signal is greater than the predetermined amplitude; and aselecting unit configured to select and output the first constant duringthe predetermined time period from a time when the count value of thecounting unit has reached the first predetermined value until a timewhen the count value has reached a second predetermined value, andselect and output the second constant when the count value of thecounting unit has reached the second predetermined value.
 5. Theadaptive filter of claim 1, wherein the output unit includes: adetecting unit configured to detect whether or not a predetermined valuewhen the amplitude of the output signal has reached the predeterminedamplitude is greater than the value indicative of the error; and aparameter output unit configured to output the first constant as theparameter when the detecting unit detects that the value indicative ofthe error is greater than the predetermined value, and output the secondconstant as the parameter when the detecting unit detects that the valueindicative of the error is smaller than the predetermined value.